Centroid & second moment of area worksheet with answers

Free printable Centroid & second moment of area worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
240 mm150 mm45 mmØ50ȳ = ?

A 240 mm × 150 mm plate has a circular hole of diameter 50 mm on its vertical centre line, with its centre 45 mm above the bottom edge. Find the height ȳ of the centroid above the bottom edge.

b = 240 mmh = 150 mmd = 50 mmhole centre: y = 45 mm
ȳ = mm
2.Easy
150 mm150 mm75 mm45 mmØ30x̄ = ?

A 150 mm × 150 mm plate has a circular hole of diameter 30 mm whose centre is 45 mm from the left edge (at mid-height). Find the distance x̄ of the centroid from the left edge.

b = 150 mmh = 150 mmd = 30 mmhole centre: x = 45 mm
x̄ = mm
3.Medium
1602020016xdimensions in mm

Find the second moment of area Ix of the T-section about the horizontal axis x through its centroid.

bf = 160 mmtf = 20 mmtw = 16 mmhw = 200 mm
Ix = × 10⁶ mm⁴
4.Medium
100 mm150 mm105 mmØ40xIx​ = ?

A 100 mm × 150 mm plate has a circular hole of diameter 40 mm on its vertical centre line, with its centre 105 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.

b = 100 mmh = 150 mmd = 40 mmhole centre: y = 105 mm
Ix = × 10⁶ mm⁴
5.Hard
100 mm240 mm84 mm60 × 30xIx​ = ?

A 100 mm × 240 mm plate has a rectangular cut-out 60 mm wide and 30 mm high, centred on the vertical centre line with its centre 84 mm above the bottom. Find the second moment of area Ix about the horizontal axis through the centroid.

b = 100 mmh = 240 mmcut-out: 60 × 30 mmhole centre: y = 84 mm
Ix = × 10⁶ mm⁴
6.Hard
2803018016xM = 50 kN·mdimensions in mm

The T-section is used as a beam with the flange on top and carries a sagging bending moment of 50 kN·m. Find the size of the bending stress σtop at the top edge.

bf = 280 mmtf = 30 mmtw = 16 mmhw = 180 mmM = 50 kN·m
σtop = MPa

Answer key

  1. 1. ȳ = 76.73 mm
  2. 2. x̄ = 75.97 mm
  3. 3. Ix = 30.13 × 10⁶ mm⁴
  4. 4. Ix = 26.76 × 10⁶ mm⁴
  5. 5. Ix = 112.5 × 10⁶ mm⁴
  6. 6. σtop = 65.22 MPa

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